Answer:
4 units
Step-by-step explanation:
The volume of a square pyramid is (a²)*h/3
256=a²*12/3
256=a²*4
256/4=a²
64=a²
a=8
Now we know that the square is 8 by 8.
The volume of a square prism is a²h
256=64h
256/64=h
h=4
Also, a square pyramid is 1/3 the volume of a square prism.
12÷3=4
The answer to the question is X=1/3
Answer: option d. C (0,3), D (0,5).
Justification:
1) The x - coordinates of the vertices A and B are shown in the diagrama, They are both - 4, so the new vertices C and D must be in a line parallel to y = - 4.
2) The y-coordinates of the vertices A and B are also shown in the diagrama. They are equal to 3 and 5 respectively.
3) We can see that the new points C and D must be over a parallel line to y = - 4 and that their distance to the points A and B has to be the same distance of the point R and S to U and T.
That distance is 4, so the line may be y = - 7 or y = 0.
4) If the line is y = 7 the points C and D would have coordinates (-7,3) and (-7,5), but this points are not among the options.
5) If the line is y = 0 the points C and D would have coordinates (0, 3) and (0,5), which is precisely the points of the option d. That is the answer.
Hi again!
2x + y > 8
The correct answer is option D
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Honestly I don't think we can solve the equation to find the answer. What we can do is to find the boundary line. (I think you know what that is) After that, shading the appropriate area.
y > -2x + 8
Again, credit to my beautiful graphing calculator. Here is how it looks like.
Given:
The graph of line.
To find:
The gradient of the line using rise/run method.
Solution:
We know that the gradient of a line is also known as slope.

Consider the two intercepts, then rise is distance between origin and y-intercept and run is the distance between origin and the x-intercept. But rise must be negative because the value of y decreased from 3 to 0.


Now,


The gradient of the line is
.
Therefore, the correct option is C.